The GNSS navigation problem is the problem of estimating the position of a GNSS user by means of the information provided by the GNSS signal as received by a GNSS user receiver.
There are several standard GNSS navigation techniques, the most common of which is absolute navigation. In absolute navigation, the navigation system computes its absolute position with no more information than that contained in the GNSS satellite signals, by means of so-called pseudo-range measurements (noisy measurements of the distance between the receiver and the GNSS satellites based on the determination of the travel time of the GNSS signals from the satellites to the receiver). For that purpose, it is necessary to synchronise the receiver clock with the GNSS system time (to which the GNSS satellite clocks are supposed to be steered to a very high accuracy). In other words, in absolute navigation mode, the receiver must estimate its clock bias in order to be able to estimate its position. Both position and clock bias are usually estimated simultaneously in a common least squares linear estimation process. The number of parameters to be estimated in this navigation mode is thus four: three position coordinates plus the clock bias.
Other standard GNSS navigation techniques include differential navigation and kinematics navigation. In both cases the receiver computes its position relative to a GNSS station, taking advantage of the GNSS signal observations acquired by the station. This eliminates the need for an accurate receiver clock synchronisation, since the receiver can combine the observations from the station with its own observations in such a way that the receiver clock bias contribution cancels out, thus allowing for a three (instead of four) parameter state estimation.
As far as the present invention is concerned, there is no difference between relative, kinematic or even absolute GNSS navigation techniques, as long as they are based on least squares estimation. So let's briefly introduce the least squares GNSS navigation technique in a generic form in which the presence or absence of the clock bias as a component of the estimation vector is transparent. This is standard theory and can be found in the literature (see e.g. “Understanding GPS: Principles and Applications”, Elliot D. Kaplan & Christopher J. Hegarty (editors), 2006), so we will not go into all the details.
In any GNSS navigation mode the estimation problem to be solved is non-linear, so as linear least squares estimation methods are going to be applied (which are also standard in GNSS navigation), the navigation problem must first be linearised. Let us call η the actual user state vector (with three or four parameters depending on the navigation mode). The linearization requires an initial guess of η that will be denoted η0, around which to differentiate the non-linear GNSS observation equations. The resulting linear estimation problem can be written as:y=H·x+ε  [Eq. 1]where:                The vector x is the state innovation x=η−η0, that is, the difference between the state guess η0 and the true state η, and hence is what must be estimated in order to solve de navigation problem.        The observation vector y is formed with the difference between the actual measurements (e.g. pseudo-range measurements in the case of absolute navigation), which are obtained from the position defined by the actual state η, and the (fictitious) measurements that would be obtained if the receiver were in the position defined by the guessed state η0.        The error vector ε is the vector of measurement errors (e.g. pseudo-range errors).        
The observation matrix H (sometimes also called geometry matrix) is the (Jacobian) matrix of partial derivatives of the non-linear GNSS observation equation in the state guess η0, and hence relates small innovations of the state around η0 with small innovations of the measurements as expected at η0.
As far as the present invention is concerned, the actual form of the non-linear GNSS observation equation or how the observation matrix H is derived from it, are not relevant topics, so we will not go into such details (which, on the other hand, are of standard use in GNSS least squares navigation and can be learned from many GNSS literature sources as, for instance, “Global Positioning System: Theory & Applications”, Bradford W. Parkinson & James J. Spilker (editors), 1996). The important fact is that H relates the state innovation, observation and error vectors as stated in equation Eq. 1.
Note that the vectors y and ε have as many coordinates as observations are available, e.g. as simultaneous pseudo-range measurements are available at a the moment in which the position is to be computed, in the case of absolute navigation, or as the number of double-differenced phase measurements in the case of kinematic navigation. It is assumed that there are n observations available. Then the vectors y and ε have n coordinates, whereas x has m coordinates and H has size n×m (m being three or four depending on the type of navigation). Note also that the vector y and the matrix H are known, the state innovation vector x is the one to be estimated and the error vector ε will always remain unknown (or otherwise it could be possible correct the errors and there would be no errors at all, which is impossible).
The least squares estimate of x is given by the well-known formula:{circumflex over (x)}=(HT·H)−1HT·y 
It provides an estimate {circumflex over (x)} of the state innovation x, which in turn provides an estimation {circumflex over (η)}=η0+{circumflex over (x)} of the state η=η0+x. The estimation error δ is the difference between the estimated state {circumflex over (η)} and the actual state η which in turn is the same as the difference between the estimated state innovation {circumflex over (x)} and the actual state innovation x:δ={circumflex over (η)}−η={circumflex over (x)}=x 
So far the basics of a standard GNSS navigation technique (GNSS navigation by means of least squares) have been described. Let us now define accurately the notion that constitutes the main concern of the present invention: the Protection Level.
The protection level (PL) is a bound, up to a given confidence level 1−α, to the error of the estimation of the GNSS position solution, i.e. a bound on the size relation between the positioning error or one of its components (e.g. vertical or horizontal component) and the residual vector resulting from the position calculation itself.
So, a protection level with confidence 1−α for the least squares navigation solution described above is a positive number PL such that:P(∥δ∥≧PL)≦αwhere P is the probability operator.
Note that δ is always unknown, and that is the reason why we want to bound it.
The concept of Protection Level is usually particularized to a subset of the coordinates of the state vector; note that δ has three spatial components (plus the clock bias component in the case of absolute navigation). If the coordinate system used is the local horizon system at {circumflex over (η)} (and so it will be assumed in what follows), then the vector δ is also expressed in local horizon coordinates, and hence its three spatial components represent the estimation errors in the directions East, North and Up (δE, δN and δU, respectively). It is not unusual that a particular GNSS application is specially interested in a bound for just one of the components (e.g. the vertical component δU, as in the case of civil aviation) or a subset of them (e.g., the horizontal components δE and δN, as in the case of electronic road fee collection).
A vertical protection level with confidence 1−α for the least squares navigation solution described above is a positive number VPL such that:P(∥δU∥≧VPL)≦α
A horizontal protection level with confidence 1−α for the least squares navigation solution described above is a positive number HPL such that:P(∥δH∥≧HPL)≦α
where
      δ    H    =      [                                        δ            E                                                            δ            N                                ]  is the horizontal component of the estimation error vector δ.
This concept of Protection Level arose as the core of the GNSS Integrity concept that was developed for Satellite Based Augmentation Systems (SBAS), such as the American WAAS or the European EGNOS among others, and has been applied specifically to those systems as well as to Ground Base Augmentation Systems (GBAS) such as LAAS. Both SBAS and GBAS are systems that provide real time corrections and integrity information applicable to GNSS observations. Civil aircrafts equipped with special GNSS navigation units can receive those corrections and apply them to their GNSS observations, as well as the integrity information, in the form of statistical bounds (i.e. bounds up to a certain statistical confidence level) to the observation errors that remain after applying the corrections. Thus the on-board GNSS unit can achieve a more accurate estimate of its position (thanks to corrections) and, moreover, can compute a Protection Level, which is a statistical bound to the remaining position error (thanks to the statistical bounds to observation errors that are broadcast by the system).
Besides, autonomous methods for computing a Protection Level (autonomous meaning that they do not depend on corrections or any extra information coming from an augmentation system such as a SBAS or a GBAS) have been defined in the frame of the so-called RAIM methods (Receiver Autonomous Integrity Monitoring). The RAIM concept aims to provide an integrity layer to the GNSS navigation process, implementing techniques for detecting and isolating faulty measurements (that is, measurements with excessive error) along with the mentioned Protection Levels for statistically bounding the position estimation error. Such PL computation methods are, however, difficult to justify from a theoretical point of view, since they rely on hypotheses that rarely hold in real world.
The present invention provides a robust and consistent—from a theoretical point of view—method for autonomously computing Protection Levels based on one single and verisimilar hypothesis, thus solving the weaknesses of previously existing methods.